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      <li class="navelem"><a class="el" href="dir_fc5e39b96a4a731194f34224fb7033b5.html">utils</a>      </li>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment"># Copyright (c) 2011</span>
<a name="l00002"></a>00002 <span class="comment">#</span>
<a name="l00003"></a>00003 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00004"></a>00004 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00005"></a>00005 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00006"></a>00006 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00007"></a>00007 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00008"></a>00008 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00009"></a>00009 <span class="comment">#</span>
<a name="l00010"></a>00010 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00011"></a>00011 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00014"></a>00014 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00015"></a>00015 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00016"></a>00016 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00017"></a>00017 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00018"></a>00018 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00019"></a>00019 <span class="comment"># SOFTWARE.</span>
<a name="l00020"></a>00020 <span class="comment">#</span>
<a name="l00021"></a>00021 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00022"></a>00022 <span class="comment">#</span>
<a name="l00023"></a>00023 
<a name="l00024"></a>00024 <span class="keyword">from</span> scipy <span class="keyword">import</span> zeros, ones, linspace, asarray
<a name="l00025"></a>00025 <span class="keyword">from</span> scipy <span class="keyword">import</span> arange, linalg
<a name="l00026"></a>00026 
<a name="l00027"></a><a class="code" href="classutils_1_1Grid_1_1Grid.html">00027</a> <span class="keyword">class </span><a class="code" href="classutils_1_1Grid_1_1Grid.html">Grid</a>:
<a name="l00028"></a>00028     <span class="stringliteral">&quot;&quot;&quot;A simple grid class that stores the details and solution of the</span>
<a name="l00029"></a>00029 <span class="stringliteral">    computational grid.&quot;&quot;&quot;</span>
<a name="l00030"></a>00030 
<a name="l00031"></a>00031     __solts__=[<span class="stringliteral">&#39;m_nx&#39;</span>, <span class="stringliteral">&#39;m_ny&#39;</span>, <span class="stringliteral">&#39;m_xmin&#39;</span>, <span class="stringliteral">&#39;m_xmax&#39;</span>, <span class="stringliteral">&#39;m_ymin&#39;</span>, <span class="stringliteral">&#39;m_ymax&#39;</span>, <span class="stringliteral">&#39;m_u&#39;</span>, <span class="stringliteral">&#39;m_old_u&#39;</span>]
<a name="l00032"></a>00032 
<a name="l00033"></a>00033     <span class="keyword">def </span>__init__(self, nx=10, ny=10, xmin=0.0, xmax=1.0,
<a name="l00034"></a>00034                  ymin=0.0, ymax=1.0):
<a name="l00035"></a>00035         self.m_xmin, self.m_xmax, self.m_ymin, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ac1968b8b54cca01dec2e42ede478c5c2">m_ymax</a> = xmin, xmax, ymin, ymax
<a name="l00036"></a>00036         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#aa622079a90e4719b08d4cb081a0608f6">m_nx</a> = nx
<a name="l00037"></a>00037         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a88426dbc9630873a80d2ea865f228d4a">m_ny</a> = ny
<a name="l00038"></a>00038         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a2977db3165e853245b1b1a91dd6ad196">m_dx</a> = float(xmax-xmin)/(nx-1)
<a name="l00039"></a>00039         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ab01b404bd24aaae6f0ab644aa46c2ae0">m_dy</a> = float(ymax-ymin)/(ny-1)
<a name="l00040"></a>00040         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a>  = zeros((nx, ny), <span class="stringliteral">&#39;d&#39;</span>)
<a name="l00041"></a>00041 
<a name="l00042"></a>00042         <span class="comment"># used to compute the change in solution in some of the methods.</span>
<a name="l00043"></a>00043         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#afbdf203cb977a92eadb1198277f80399">m_old_u</a> = self.m_u.copy()
<a name="l00044"></a>00044 
<a name="l00045"></a><a class="code" href="classutils_1_1Grid_1_1Grid.html#a3b4aff84601c4b63e7b1a9d984100f57">00045</a>     <span class="keyword">def </span><a class="code" href="classutils_1_1Grid_1_1Grid.html#a3b4aff84601c4b63e7b1a9d984100f57">setBCFunc</a>(self, func):
<a name="l00046"></a>00046       <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00047"></a>00047 <span class="stringliteral">        When use as a finite difference mesh, Sets the BC given a function of two variables.</span>
<a name="l00048"></a>00048 <span class="stringliteral">      &quot;&quot;&quot;</span>
<a name="l00049"></a>00049       m_xmin, ymin = self.m_xmin, self.m_ymin
<a name="l00050"></a>00050       xmax, ymax = self.m_xmax, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ac1968b8b54cca01dec2e42ede478c5c2">m_ymax</a>
<a name="l00051"></a>00051 
<a name="l00052"></a>00052       x = arange(m_xmin, xmax + self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a2977db3165e853245b1b1a91dd6ad196">m_dx</a>*0.5, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a2977db3165e853245b1b1a91dd6ad196">m_dx</a>)
<a name="l00053"></a>00053       y = arange(ymin, ymax + self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ab01b404bd24aaae6f0ab644aa46c2ae0">m_dy</a>*0.5, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ab01b404bd24aaae6f0ab644aa46c2ae0">m_dy</a>)
<a name="l00054"></a>00054 
<a name="l00055"></a>00055       self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a>[0 ,:] = func(m_xmin, y)
<a name="l00056"></a>00056       self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a>[-1,:] = func(xmax, y)
<a name="l00057"></a>00057       self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a>[:, 0] = func(x, ymin)
<a name="l00058"></a>00058       self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a>[:,-1] = func(x, ymax)
<a name="l00059"></a>00059 
<a name="l00060"></a>00060     <span class="keyword">def </span>get_grid(self):
<a name="l00061"></a>00061       <span class="keywordflow">return</span> self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a>
<a name="l00062"></a>00062 
<a name="l00063"></a>00063     <span class="keyword">def </span>getBox(self):
<a name="l00064"></a>00064       <span class="keywordflow">return</span> [self.m_xmin, self.m_xmax, self.m_ymin, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ac1968b8b54cca01dec2e42ede478c5c2">m_ymax</a>]
<a name="l00065"></a>00065 
<a name="l00066"></a>00066     <span class="keyword">def </span>getDeltaXY(self):
<a name="l00067"></a>00067       <span class="keywordflow">return</span> [self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a2977db3165e853245b1b1a91dd6ad196">m_dx</a>, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ab01b404bd24aaae6f0ab644aa46c2ae0">m_dy</a>]
<a name="l00068"></a>00068 
<a name="l00069"></a>00069     <span class="keyword">def </span>getNxNy(self):
<a name="l00070"></a>00070       <span class="keywordflow">return</span> [self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#aa622079a90e4719b08d4cb081a0608f6">m_nx</a>, self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a88426dbc9630873a80d2ea865f228d4a">m_ny</a>]
<a name="l00071"></a>00071 
<a name="l00072"></a><a class="code" href="classutils_1_1Grid_1_1Grid.html#a6e9af7f58eb43c4db12daf9cd0b34ed0">00072</a>     <span class="keyword">def </span><a class="code" href="classutils_1_1Grid_1_1Grid.html#a6e9af7f58eb43c4db12daf9cd0b34ed0">lexPositions</a>(self, i, j):
<a name="l00073"></a>00073       <span class="stringliteral">&quot;&quot;&quot; return the lexicographic position of point (i, j)</span>
<a name="l00074"></a>00074 <span class="stringliteral">          Dirichlet BC.</span>
<a name="l00075"></a>00075 <span class="stringliteral">      &quot;&quot;&quot;</span>
<a name="l00076"></a>00076       assert( 0 &lt; i <span class="keywordflow">and</span> i &lt; self.nx )
<a name="l00077"></a>00077       assert( 0 &lt; j <span class="keywordflow">and</span> j &lt; self.ny )
<a name="l00078"></a>00078       <span class="keywordflow">return</span> (self.nx-2)*(i-1)+(j-1)
<a name="l00079"></a>00079 
<a name="l00080"></a><a class="code" href="classutils_1_1Grid_1_1Grid.html#a1fdd7c2ade1050bea2509ecc7ab803ab">00080</a>     <span class="keyword">def </span><a class="code" href="classutils_1_1Grid_1_1Grid.html#a1fdd7c2ade1050bea2509ecc7ab803ab">computeError</a>(self):
<a name="l00081"></a>00081      <span class="stringliteral">&quot;&quot;&quot;Computes absolute error using an L2 norm for the solution.</span>
<a name="l00082"></a>00082 <span class="stringliteral">        This requires that self.m_u and self.m_m_old_u must be appropriately</span>
<a name="l00083"></a>00083 <span class="stringliteral">        setup.</span>
<a name="l00084"></a>00084 <span class="stringliteral">     &quot;&quot;&quot;</span>
<a name="l00085"></a>00085      v = (self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#adf9adc736212856f1b5cd5778cfa39b3">m_u</a> - self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#afbdf203cb977a92eadb1198277f80399">m_old_u</a>).flat
<a name="l00086"></a>00086      <span class="keywordflow">return</span> linalg.norm(v)
<a name="l00087"></a>00087 
<a name="l00088"></a><a class="code" href="classutils_1_1Grid_1_1Grid.html#a38cbf1f45f1eedbbd853e87e3141ec03">00088</a>     <span class="keyword">def </span><a class="code" href="classutils_1_1Grid_1_1Grid.html#a38cbf1f45f1eedbbd853e87e3141ec03">getTriangle</a>(self, i, j, posi):
<a name="l00089"></a>00089       <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00090"></a>00090 <span class="stringliteral">        returns the coordinates of the triangle</span>
<a name="l00091"></a>00091 <span class="stringliteral">        with appex (i, j) and in the posi quadrant.</span>
<a name="l00092"></a>00092 <span class="stringliteral">        posi \in [0, 3]</span>
<a name="l00093"></a>00093 <span class="stringliteral">        0 ~ up | up</span>
<a name="l00094"></a>00094 <span class="stringliteral">        1 ~ up | do</span>
<a name="l00095"></a>00095 <span class="stringliteral">        2 ~ do | do</span>
<a name="l00096"></a>00096 <span class="stringliteral">        3 ~ do | do</span>
<a name="l00097"></a>00097 <span class="stringliteral">      &quot;&quot;&quot;</span>
<a name="l00098"></a>00098 
<a name="l00099"></a>00099       assert( 0 &lt;= i <span class="keywordflow">and</span> i &lt; self.nx )
<a name="l00100"></a>00100       assert( 0 &lt;= j <span class="keywordflow">and</span> j &lt; self.ny )
<a name="l00101"></a>00101       assert( 0 &lt;= posi <span class="keywordflow">and</span> posi &lt; 4 )
<a name="l00102"></a>00102 
<a name="l00103"></a>00103       neig ={ 0 : [1, 1],
<a name="l00104"></a>00104               1 : [-1, 1],
<a name="l00105"></a>00105               2 : [-1, -1],
<a name="l00106"></a>00106               3 : [1, -1]
<a name="l00107"></a>00107             }[posi]
<a name="l00108"></a>00108 
<a name="l00109"></a>00109       <span class="keywordflow">if</span> 0 &gt; i+neig[0] <span class="keywordflow">or</span> i+neig[0] &gt; self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#aa622079a90e4719b08d4cb081a0608f6">m_nx</a>:
<a name="l00110"></a>00110         <span class="keywordflow">return</span> <span class="keywordtype">None</span>
<a name="l00111"></a>00111 
<a name="l00112"></a>00112       <span class="keywordflow">if</span> 0 &gt; j+neig[1] <span class="keywordflow">or</span> j+neig[1] &gt; self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a88426dbc9630873a80d2ea865f228d4a">m_ny</a>:
<a name="l00113"></a>00113         <span class="keywordflow">return</span> <span class="keywordtype">None</span>
<a name="l00114"></a>00114 
<a name="l00115"></a>00115       dx = self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a2977db3165e853245b1b1a91dd6ad196">m_dx</a>
<a name="l00116"></a>00116       dy = self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#ab01b404bd24aaae6f0ab644aa46c2ae0">m_dy</a>
<a name="l00117"></a>00117 
<a name="l00118"></a>00118       tria = zeros( (3, 2), <span class="stringliteral">&#39;float&#39;</span>)
<a name="l00119"></a>00119       ll   = asarray([self.m_xmin, self.ymin])
<a name="l00120"></a>00120       tria[0, :] = asarray( [i*dx, j*dy] + ll )
<a name="l00121"></a>00121 
<a name="l00122"></a>00122       <span class="keywordflow">if</span> 0 == posi:
<a name="l00123"></a>00123         tria[1, :] = tria[0, :] + asarray([dx, 0])
<a name="l00124"></a>00124         tria[2, :] = tria[0, :] + asarray([0 , dy])
<a name="l00125"></a>00125       <span class="keywordflow">if</span> 1 == posi:
<a name="l00126"></a>00126         tria[1, :] = tria[0, :] + asarray([0  , dy])
<a name="l00127"></a>00127         tria[2, :] = tria[0, :] + asarray([-dx, 0])
<a name="l00128"></a>00128       <span class="keywordflow">if</span> 2 == posi:
<a name="l00129"></a>00129         tria[1, :] = tria[0, :] + asarray([-dx, 0])
<a name="l00130"></a>00130         tria[2, :] = tria[0, :] + asarray([0, -dy])
<a name="l00131"></a>00131       <span class="keywordflow">if</span> 3 == posi:
<a name="l00132"></a>00132         tria[1, :] = tria[0, :] + asarray([0  , -dy])
<a name="l00133"></a>00133         tria[2, :] = tria[0, :] + asarray([-dx, 0])
<a name="l00134"></a>00134 
<a name="l00135"></a>00135       <span class="keywordflow">return</span> tria
<a name="l00136"></a>00136 
<a name="l00137"></a>00137 <span class="keyword">class </span>Grid1D(object):
<a name="l00138"></a>00138     __solts__=[<span class="stringliteral">&#39;m_nSegs&#39;</span>, <span class="stringliteral">&#39;m_x&#39;</span>, <span class="stringliteral">&#39;m_xmin&#39;</span>, <span class="stringliteral">&#39;m_xmax&#39;</span>]
<a name="l00139"></a>00139     <span class="keyword">def </span>__init__(self, nSegs = 10, xmin=0.0, xmax=1.0):
<a name="l00140"></a>00140 
<a name="l00141"></a>00141         self.m_nSegs = nSegs
<a name="l00142"></a>00142         self.m_x  = asarray(linspace(xmin, xmax, nSegs+1, <span class="stringliteral">&#39;True&#39;</span>))
<a name="l00143"></a>00143         self.<a class="code" href="classutils_1_1Grid_1_1Grid.html#a2977db3165e853245b1b1a91dd6ad196">m_dx</a> = float(xmax-xmin)/nSegs
<a name="l00144"></a>00144         (self.m_xmin, self.m_xmax) = (xmin, xmax)
<a name="l00145"></a>00145 
<a name="l00146"></a>00146     <span class="keyword">def </span>get_nsegs(self):
<a name="l00147"></a>00147         <span class="keywordflow">return</span> self.m_nSegs
<a name="l00148"></a>00148 
<a name="l00149"></a>00149     <span class="keyword">def </span>getSegments(self):
<a name="l00150"></a>00150         <span class="keywordflow">return</span> [asarray([self.m_x[i], self.m_x[i+1]], <span class="stringliteral">&#39;float&#39;</span>) <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(self.m_nSegs)]
<a name="l00151"></a>00151 
<a name="l00152"></a>00152     <span class="keyword">def </span>getDx(self):
<a name="l00153"></a>00153         <span class="keywordflow">return</span> self.m_x[1:]-self.m_x[:-1]
<a name="l00154"></a>00154 
<a name="l00155"></a>00155     <span class="keyword">def </span>getNumSegs(self):
<a name="l00156"></a>00156         <span class="keywordflow">return</span> self.m_nSegs
<a name="l00157"></a>00157 
<a name="l00158"></a>00158     <span class="keyword">def </span>get_grid(self):
<a name="l00159"></a>00159         <span class="keywordflow">return</span> self.m_x
<a name="l00160"></a>00160 
<a name="l00161"></a>00161     <span class="keyword">def </span>getRange(self):
<a name="l00162"></a>00162         <span class="keywordflow">return</span> (self.m_xmin, self.m_xmax)
<a name="l00163"></a>00163 
<a name="l00164"></a>00164 
<a name="l00165"></a>00165 
<a name="l00166"></a>00166 
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